Geospatial modeling system providing void inpainting based upon selectable inpainting functions and related methods

ABSTRACT

A geospatial modeling system may include a geospatial model data storage device and a processor. The processor may cooperate with the geospatial model data storage device for selecting and transforming a reference sample of a geospatial model frequency domain data set into a corresponding reference sample geospatial model spatial domain data set, and inpainting data into at least one void of the geospatial model frequency domain data set based upon an initial selected inpainting function from among a plurality of different inpainting functions. The processor may further select and transform a test sample of the inpainted geospatial model frequency domain data set into a corresponding test sample geospatial model spatial domain data set, and compare the reference sample geospatial model spatial domain data set and the test sample geospatial model spatial domain data set to determine whether to repeat the inpainting using a different inpainting function from among the plurality thereof.

FIELD OF THE INVENTION

The present invention relates to the field of data modeling, and, moreparticularly, to modeling systems such as geospatial modeling systemsand related methods.

BACKGROUND OF THE INVENTION

Topographical models of geographical areas may be used for manyapplications. For example, topographical models may be used in flightsimulators and for planning military missions. Furthermore,topographical models of man-made structures (e.g., cities) may beextremely helpful in applications such as cellular antenna placement,urban planning, disaster preparedness and analysis, and mapping, forexample.

Various types and methods for making topographical models are presentlybeing used. One common topographical model is the digital elevation map(DEM). A DEM is a sampled matrix representation of a geographical areawhich may be generated in an automated fashion by a computer. In a DEM,coordinate points are made to correspond with a height value. DEMs aretypically used for modeling terrain where the transitions betweendifferent elevations (e.g., valleys, mountains, etc.) are generallysmooth from one to a next. That is, DEMs typically model terrain as aplurality of curved surfaces and any discontinuities therebetween arethus “smoothed” over. Thus, in a typical DEM no distinct objects arepresent on the terrain.

One particularly advantageous 3D site modeling product is RealSite®which is a software plugin in Harris' Multi-image exploitation tool fromthe present Assignee Harris Corp. RealSite® may be used to registeroverlapping images of a geographical area of interest, and extract highresolution DEMs using stereo and nadir view techniques. RealSite®provides a semi-automated process for making three-dimensional (3D)topographical models of geographical areas, including cities, that haveaccurate textures and structure boundaries. Moreover, RealSite® modelsare geospatially accurate. That is, the location of any given pointwithin the model corresponds to an actual location in the geographicalarea with very high accuracy. The data used to generate RealSite® modelsmay include aerial and satellite photography, electro-optical, infrared,and light detection and ranging (LIDAR), for example. Another similarsystem from Harris Corp. is LiteSite®. LiteSite® models provideautomatic extraction of ground, foliage, and urban digital elevationmodels (DEMs) from LIDAR and IFSAR imagery. LiteSite® can be used toproduce affordable, geospatially accurate, high-resolution 3-D models ofbuildings and terrain.

U.S. Pat. No. 6,654,690 to Rahmes et al., which is also assigned to thepresent Assignee and is hereby incorporated herein in its entirety byreference, discloses an automated method for making a topographicalmodel of an area including terrain and buildings thereon based uponrandomly spaced data of elevation versus position. The method includesprocessing the randomly spaced data to generate gridded data ofelevation versus position conforming to a predetermined position grid,processing the gridded data to distinguish building data from terraindata, and performing polygon extraction for the building data to makethe topographical model of the area including terrain and buildingsthereon.

In many instances there will be voids or gaps in the data used togenerate a geospatial or other model. The voids negatively affect thequality of the resulting model, and thus it is desirable to compensatefor these voids while processing the data, if possible. Variousinterpolation techniques are generally used for filling in missing datain a data field. One such technique is sinc interpolation, which assumesthat a signal is band-limited. While this approach is well suited forcommunication and audio signals, it may not be well suited for 3D datamodels. Another approach is polynomial interpolation. This approach issometimes difficult to implement because the computational overhead maybecome overly burdensome for higher order polynomials, which may benecessary to provide desired accuracy.

One additional interpolation approach is spline interpolation. Whilethis approach may provide a relatively high reconstruction accuracy,this approach may be problematic to implement in a 3D data model becauseof the difficulty in solving a global spline over the entire model, andbecause the required matrices may be ill-conditioned. One furtherdrawback of such conventional techniques is that they tend to blur edgecontent, which may be a significant problem in a 3D topographical model.

Another approach for filling in regions within an image is set forth inU.S. Pat. No. 6,987,520 to Criminisi et at. This patent discloses anexemplar-based filling system which identifies appropriate fillingmaterial to replace a destination region in an image and fills thedestination region using this material. This is done to alleviate orminimize the amount of manual editing required to fill a destinationregion in an image. Tiles of image data are “borrowed” from theproximity of the destination region or some other source to generate newimage data to fill in the region. Destination regions may be designatedby user input (e.g., selection of an image region by a user) or by othermeans (e.g., specification of a color or feature to be replaced). Inaddition, the order in which the destination region is filled by exampletiles may be configured to emphasize the continuity of linear structuresand composite textures using a type of isophote-driven image-samplingprocess.

Another way in which geospatial model data can end up with voids thereinis when the data is collected in the frequency domain, as is the casewith Synthetic Aperture Radar (SAR) data collection. That is, a SARreturns a map or representation of radar reflectivity including bothamplitude and phase over a plurality of different frequencies. However,due to interference from existing signal sources, during some SAR scanscertain frequency bands may experience interference in the resulting SARdata. Moreover, the operator of the SAR may have to intentionally omitor block certain frequency bands in certain geographical areas from thescan to avoid interfering with such communication sources. Further,hardware malfunctions may result in pulse dropouts. In each of thesecases, the result is that the frequency domain representation of thearea of interest will have gaps or voids therein, which when convertedto the spatial domain cause the resulting geospatial model image to bedistorted.

Generally speaking, various approaches have been used to address theeffects of interference in frequency domain data. One approach is to uselinear interpolation. Super resolution and/or iterative convolutiontechniques have also been used which assume a point like target in theimage. Moreover, hardware approaches have also been implemented to altermode hopping to avoid interference or listening on pilot pulses tocharacterize the interference.

Another approach to interference suppression in SAR images is set forthin an article entitled “Interference Suppression in Synthesized SARImages” by Reigber et al., IEEE Geoscience and Remote Sensing Letters,vol. 2, no. 1, January 2005. This article proposes an interferencesuppression approach that relies on the transformation of synthesizedSAR images into a representation where common raw-data interferencefiltering methods can be applied. More particularly, this approach usesa posteriori filtering.

Despite the advantages such prior art approaches may provide in certainapplications, further advancements may be desirable for filling voids ingeospatial and other model data.

SUMMARY OF THE INVENTION

In view of the foregoing background, the present disclosure presents amodeling system, such as a geospatial modeling system, and relatedmethods which may advantageously fill voids within model data andrelated methods.

This and other objects, features, and advantages are provided by ageospatial modeling system which may include a geospatial model datastorage device and a processor. The processor may cooperate with thegeospatial model data storage device for selecting and transforming areference sample of a geospatial model frequency domain data set into acorresponding reference sample geospatial model spatial domain data set,and inpainting data into at least one void of the geospatial modelfrequency domain data set based upon an initial selected inpaintingfunction from among a plurality of different inpainting functions. Theprocessor may further cooperate with the geospatial model data storagedevice for selecting and transforming a test sample of the inpaintedgeospatial model frequency domain data set into a corresponding testsample geospatial model spatial domain data set, and comparing thereference sample geospatial model spatial domain data set and the testsample geospatial model spatial domain data set to determine whether torepeat the inpainting using a different inpainting function from amongthe plurality thereof.

More particularly, the inpainting functions may be based upon differentinpainting boundary geometries and/or different inpainting models, forexample. By way of example, the different inpainting models may compriseat least one of a functional partial differential equation model and astochastic model. The processor may further cooperate with thegeospatial model storage device for transforming the inpaintedgeospatial model frequency domain data set into a geospatial modelspatial domain data set. A display may also be coupled to the processorfor displaying the geospatial model spatial domain data set.

The processor may determine whether to repeat the inpainting using adifferent inpainting function based upon a threshold similarity betweenthe test sample and the reference sample. By way of example, thegeospatial model frequency domain data set may comprise syntheticaperture radar (SAR) data. The geospatial model frequency domain dataset may also comprise K-space data, for example.

In addition, the processor may inpaint by propagating contour data fromoutside the at least one void along a direction of lines of constantcontour from outside the at least one void into the at least one void.More specifically, the processor may iteratively propagate the contourdata from outside the at least one void into the at least one void. Byway of example, the contour data may comprise at least one of phase andamplitude data.

A geospatial modeling method aspect may include selecting andtransforming a reference sample of a geospatial model frequency domaindata set into a corresponding reference sample geospatial model spatialdomain data set, and inpainting data into at least one void of thegeospatial model frequency domain data set based upon an initialselected inpainting function from among a plurality of differentinpainting functions. The method may further include selecting andtransforming a test sample of the inpainted geospatial model frequencydomain data set into a corresponding test sample geospatial modelspatial domain data set, and comparing the reference sample geospatialmodel spatial domain data set and the test sample geospatial modelspatial domain data set to determine whether to repeat the inpaintingusing a different inpainting function from among the plurality thereof.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic block diagram of a data modeling system inaccordance with the invention.

FIGS. 2A and 2B are K-space and image space representations,respectively, of a non-distorted SAR data set.

FIGS. 3A and 3B are K-space and image space representations,respectively, of a distorted version of the SAR data set illustrated inFIGS. 2A and 2B.

FIG. 4 is the image space representation of FIG. 3B with a window gridoverlay illustrating a windowing scheme in accordance with an aspect ofthe invention.

FIGS. 5A and 5B are K-space and image space representations,respectively, of a spatial window of the distorted image space data setof FIG. 4.

FIG. 6 is an image space representation of a plurality of scattererpoints illustrating another windowing technique in accordance with analternative embodiment.

FIGS. 7A-7E are respective K-space representations of each windowedimage space scatterer point of FIG. 6.

FIGS. 8A-8E are the K-space representations of FIGS. 7A-7E afterinpainting.

FIG. 9 is a reconstructed image space representation generated from theinpainted K-space data sets of FIGS. 8A-8E.

FIG. 10 is a series of scaled K-space wavelet representations of theK-space data set of FIG. 3A.

FIG. 11 is the K-space representation of FIG. 3A with a window gridoverlay illustrating a windowing scheme for spectral interpolation inaccordance with another aspect of the invention.

FIG. 12 is a K-space representation of a portion of FIG. 3R illustratingan alternative windowing scheme for spectral interpolation in accordancewith another aspect of the invention.

FIG. 13 is a K-space representation of a corrupted SAR data setillustrating the use of different inpainting boundary geometries.

FIGS. 14-21 are flow diagrams illustrating various model data windowing,inpainting, and/or reconstruction method aspects in accordance with theinvention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention will now be described more fully hereinafter withreference to the accompanying drawings, in which preferred embodimentsof the invention are shown. This invention may, however, be embodied inmany different forms and should not be construed as limited to theembodiments set forth herein. Rather, these embodiments are provided sothat this disclosure will be thorough and complete, and will fullyconvey the scope of the invention to those skilled in the art. Likenumbers refer to like elements throughout, and prime notation is used toindicate similar elements in alternative embodiments.

Referring initially to FIG. 1, a modeling system 30, such as ageospatial modeling system, illustratively includes a model data storagedevice 31 for storing geospatial model data and a processor 32. By wayof example, the processor 32 may be a central processing unit (CPU) of aPC, Mac, Sun, or other computing workstation, for example. A display 33may be coupled to the processor 32 for displaying modeling data. Theprocessor 32 advantageously reconstructs or repairs corrupted modeldata, such as geospatial model data, by inpainting voids in the data, aswill be discussed further below. To this end, the processor 32illustratively includes a windowing/transforming module 34, aninpainting module 40, and a reconstruction module 41. While thesemodules are shown and described as separate components for clarity ofreference, those skilled in the art will appreciate that the variousfunctions of these components may be implemented with a combination ofhardware and software, and that these software components may beincluded in the same overall software application, for example.

Turning additionally to FIGS. 2A-2B, an exemplar synthetic apertureradar (SAR) geospatial data set is shown for a non-corrupted ornon-distorted data capture. That is, FIGS. 2A and 2B represent the idealcase in which no holes or voids in the data have occurred during datacapture, such as from interference, notched frequencies, equipmentmalfunctions, etc., as will be appreciated by those skilled in the art.In particular, the SAR data capture shown is of the U.S. Capitolbuilding.

Generally speaking, one or more data captures of a particular geospatialarea of interest are performed to obtain 3D elevation versus positiondata. The data capture may be performed using various techniques, suchas stereo optical imagery, Light Detecting And Ranging (LIDAR), SAR orInterferometric Synthetic Aperture Radar (IFSAR), etc. Generallyspeaking, the data will be captured from nadir views of the geographicalarea of interest by airplanes, satellites, etc., as will be appreciatedby those skilled in the art. However, oblique images of a geographicalarea of interest may also be used in addition to or instead of theimages to add additional 3D detail to a geospatial model. It should alsobe noted that the types of data to which the inpainting techniquesdescribed below may be applied are not limited to geospatial model data.Rather, these techniques may also be applied to other types of modeldata that may be represented and processed in the frequency domain orK-space, such as magnetic resonance imaging (MRI) data, for example.

FIGS. 3A and 3B show the effects of voids 39 in the K-space geospatialdata 37, which results in a blurred image space data set 38. Theprocessor 32 advantageously uses various inpainting techniques to fillin or repair the voids 39 in frequency data sets, such as theillustrated K-space data set 38, to thereby achieve a reconstructedcorresponding image space data set that more closely resembles theuncorrupted image space data set 35. By way of background, exemplaryinpainting techniques that may be implemented by the processor 32 areset forth in co-pending U.S. patent application Ser. No. 11/458,811 toRahmes et al., which is assigned to the present Assignee and is herebyincorporated herein in its entirety by reference.

Further inpainting aspects are now described with reference to FIGS. 4-9and 14-15. While in some implementations an entire data set may beinpainted as a whole to provide desired reconstruction accuracy, inother cases there may be a need to “smooth” the data so that the variousinpainting model functions can provide more accurate datareconstruction. Beginning at Block 160, a spatial domain data set, suchas the geospatial spatial domain data 38 may advantageously be dividedinto a plurality of windows 50 (herein referred to as “windowed” or“windowing”) by the windowing module 34. It should be noted thatdepending upon the format of the model data stored in the model datastorage device 31 (i.e., if the collected/stored data is frequencydomain or K-space data), the windowing module 34 may first transform thedata to the spatial domain prior to performing windowing operations.

One of the windows 50 is shown in greater detail in FIG. 5A. Thewindowed image space data set 50 results in a corresponding K-space dataset 55 (FIG. 5B) when transformed to K-space which, while having areduced resolution with respect to the overall K-space data set 37 (FIG.3A), generally has smoother phase and/or amplitude values than theoverall K-space data set. This is because less frequency voids areincluded in the K-space data set, so there is less “smearing” caused bythe voided data being spread throughout the K-space data set, as will beappreciated by those skilled in the art. Stated alternatively, there areless discontinuities in the phase/amplitude values of the geospatialK-space data set 55 than in the overall K-space data set 37. Withpartial differential equation (PDE) based inpainting models, forexample, it may be difficult to obtain derivatives for data sets withlarge numbers of phase/amplitude discontinuities, as will also beappreciated by those skilled in the art.

The windowing scheme used in FIG. 4 is a relatively straightforwardgrid, in which the geospatial image data set 38 is divided into aplurality of equally sized squares as shown. Different window sizes andgeometries are also possible in some embodiments. This approach may beconsidered mathematically as follows:

-   -   f(x,y) represents the image, and the image domain is partitioned        into mn squares, indexed by ij, 1≦i≦m, 1≦j≦n; let χ_(ij)(x,y) be        the characteristic/windowing function of each sub squarer and        ƒ(x,y)=Σƒ(x,y)χ_(y)(x,y)

Moreover, other windowing techniques may also be used. One suchtechnique is illustrated in FIGS. 6-9, wherein rather than dividing anentire spatial domain data set into windows, windows are instead placedaround the most problematic portions of the spatial domain data set,such as the five scatterer points included in the “top left,” “topright,” “middle,” “bottom left,” and “bottom right” windows in FIG. 6.The corresponding frequency domain (i.e., K-space) data sets 80 a-80 ecorresponding to these five spatial domain scatterer point windows areshown in FIGS. 7A-7E, respectively. Each includes a respective void 81a-81 e.

Once the windowed geospatial model spatial domain data sets 50 aretransformed to define corresponding geospatial model frequency domaindata sets 55, at Block 162, then the inpainting module 40 mayadvantageously begin inpainting the void(s) therein, at Block 163, todefine inpainted geospatial model frequency domain data sets 90 a-90 e,which for the above-noted scatterer windows are shown in FIGS. 8A-8E.Generally speaking, the voids 81 a-81 e are inpainted by iterativelypropagating contour (i.e., phase/amplitude) data from outside a givenvoid into the given void (Blocks 163′ and 166′). More particularly, theprocessor 22 inpaints by propagating contour data from outside the givenvoid along a direction of lines of constant elevation contour fromoutside the given void into the void. More particularly, the lines ofconstant elevation contour may be based upon isophote and gradientdirections at given points along the void boundary, as discussed furtherin the above-noted '811 application.

Various inpainting models may be used that are based upon differentfluid flow modeling equations, such as PDEs, Stochastic, etc. By way ofexample, one general inpainting equation that may be used by theinpainting module 40 for the inpainting operations is the following:

$\begin{matrix}{{{{\frac{\partial I}{\partial t} + {{\nabla^{\bot}I} \cdot {\nabla\left( {\Delta \; I} \right)}}} = {{div}\left( {{g\left( {{\nabla I}} \right)}{\nabla I}} \right)}},{where}}\mspace{14mu} {{{\Delta \; I} = {\nabla^{2}I}},{{i.e.\mspace{11mu} {the}}\mspace{14mu} {Laplacian}}}} & (1)\end{matrix}$

In equation (1),

$\frac{\partial I}{\partial t}$

is a time component of the equation,

∇^(⊥)I•∇(ΔI) div(g(|∇I|)∇I)

is a convective component, and is an anisotropic diffusion component, aswill be appreciated by those skilled in the art.

Another inpainting approach is based upon Navier-Stokes' equations, oneimplementation of which is as follows:

v _(t) +v•∇v=−∇p+vΔv, ∇•v=0

where

${{\nabla^{\bot}\Psi} = {v = {\langle{{- \frac{\partial\Psi}{\partial y}},\frac{\partial\Psi}{\partial x}}\rangle}}},\Psi$

is the Stream Function;

∇×(v _(t) +v•∇v)=∇×(−∇p+vΔv),

where ∇×v=ω, thus, ω_(t)+v•∇ω=v∇²ω,

ω=∇²Ψ (i.e., the Laplacian); and the Stream Function is defined as:

Ψ=1(x,y)→r,

where rε

and x, yεN.

Other inpainting models may be based upon Bertozzi, Sapiro, andBartalmio equations, for example, as will be appreciated by thoseskilled in the art. An exemplary functional PDE inpainting approach isas follows:

For each k, where k represents the different scales of the wavelengthdecomposition,

${{\frac{\partial v_{k}}{\partial t} + {v_{k} \cdot {\nabla{F_{k}\left( {t,x,y,v_{k},v_{X}} \right)}}}} = 0},$

where

F_(k)(t, x, y, v_(k)v_(X)) = α_(k)δ_(mk)∫_(N_(F)^(k))∫_((0, 0))v_(X)(t, ξ, η)ξη + β_(k)v_(k)(x, y), v_(X)(t, ξ, η) = v(t, x + ξ, y + η), andv_(k)(x, y) = u(x, y) + c_(k)(x, y)n_(k)(x, y);

for (ξ,η)εN_(r) ^(k)(0,0), the δ_(mk) is the Kronecker delta.

α_(mk), β_(k) are suitably chosen constants and the function c_(k)(x,y)is a weight function that appropriately turns the noise term “on” or“off”.

Also, N_(r) ^(k)(0,0) is a neighborhood of the origin.

The inpainted geospatial model frequency domain data sets 90 a-90 e maythen be reconstructed by the reconstruction module 41 into an overallgeospatial model spatial domain data set, at Block 164, thus concludingthe illustrated method. (Block 165). Thereafter, it may be furthertransformed to an overall reconstructed geospatial model spatial domaindata set 100 (FIG. 9), at Block 167, for display on the display 33(Block 168′), as will be appreciated by those skilled in the art.

Turning now additionally to FIGS. 10 and 16-17, another technique whichmay be used by the processor 32 to provide still greater accuracy whenreconstructing holes in frequency/K-space data through inpainting is tofirst perform wavelet decomposition on the given frequency/K-space dataset(s) prior to inpainting. More particularly, beginning at Block 180,the geospatial model frequency domain data set 50 is decomposed by thewindowing/transforming module 34 to define scaled versions 91 a-91 ethereof, as seen in FIG. 10 (Block 181). As will be appreciated by thoseskilled in the art, wavelet decomposition generates an expansion serieswith different order terms that represent different levels orresolutions (i.e., scales) of the overall geospatial model frequencydomain data set 50. As such, the inpainting module 40 may then inpaintdata into the voids 39 of each of the scaled data sets 91 a-91 e, atBlock 182, and the inpainted scaled versions may then be reconstructed(i.e., amalgamated) into a reconstructed geospatial model frequencydomain data set (Block 183) by the reconstruction module, thusconcluding the method illustrated in FIG. 18 (Block 184).

By first performing wavelet decomposition and then performing inpaintingon each of the scaled versions 91 a-91 e of the K-space data set 37,this may advantageously provide more accurate inpainting results thansimply inpainting the unscaled K-space data set in its entirety. Anexemplary wavelet decomposition equation that may be used is as follows:

ƒ(X)=Σ^(C) _(jk)ψ_(jk)(X)   (2)

-   -   where Ψ_(jk)(X) are two dimensional wavelets        More particularly, the wavelet decomposition operations may be        considered as follows:

for each i, j is

F(ƒ(x,y)χ_(ij)(x,y))=Σ^(C) _(mm)φ_(mm)(x,y)+d _(mm)ψ¹ _(mm)(x,y)+e_(mm)ψ² _(mm)(x,y)+ƒ_(mm)ψ³ _(mm)(x,y),

where φ_(mm)(x,y), ψ¹ _(mm)(x,y), ψ² _(mm)(x,y), ψ³ _(mm)(x,y), are twodimensional wavelets. K space data is Unpainted using the FPDE modelwith a “noise like” term, which is generally applicable to low scales,and K space data inpainted by a PDE model with a “noise like” term isgenerally applicable to high scales. The amalgam of the inpaintedversions is taken to form the repaired image.

While the above-noted wavelet decomposition approach need not be used inconjunction with the windowing operations described above in allembodiments, in some embodiments it may be desirable to perform thespatial windowing followed by transformation of the windowed data setsto corresponding frequency domain data sets prior to waveletdecomposition (Blocks 190′-191′). Here again, the inpainting operationsmay be performed iteratively (Blocks 182′, 192′), and the reconstructedgeospatial model frequency domain data set may be transformed into anoverall reconstructed geospatial model spatial domain data set fordisplay on the display 33 (Blocks 193′, 194′), as similarly discussedabove.

In accordance with another advantageous aspect now described withreference to FIGS. 11, 12, 18, and 19, an approach for determining whendesired accuracy has been obtained so that the iterative inpaintingoperations can be stopped is now described. Beginning at Block 200, areference sample 110 r of the geospatial model frequency data set 55 isselected and transformed into a corresponding reference samplegeospatial model spatial domain data set, at Block 201. In oneembodiment, the reference sample 110 r may be selected using arelatively straightforward windowing approach similar to that describedabove, but instead of using a grid to window spatial domain data, thegrid here is instead applied to the frequency domain data set 55 todefine a plurality of frequency domain windows or data sets 110. Again,different grid shapes and sizes may be used in different embodiments.Preferably, the reference sample data set 110 r will be one whichincludes little or no voids, as this will provide a more accuratecorresponding spatial data set to use as a reference in subsequentoperations.

The inpainting module 40 iteratively inpaints data into one or morevoids in the geospatial frequency domain data set 55, as discussedfurther above, at Block 202. Furthermore, a test sample 110 t of theinpainted geospatial model frequency domain data set 55 is selected andtransformed into a corresponding test sample geospatial model spatialdomain data set, at Block 203. More particularly, the test sample 110 tis preferably from a voided area where data has been inpainted. As such,the processor 32 can advantageously compare the spatial domain referencesample 110 r and test sample 110 t to determine whether to stop theiterative inpainting within the test sample area, at Blocks 204-205,thus concluding the illustrated method (Block 206).

In particular, the comparison may involve comparison of a resolutionlevel of the test sample 110 t to determine if it has achieved a certainthreshold level of the reference sample 110 r resolution. For example,if the accuracy of the test sample 110 t achieves a resolution level of80% of that of the reference sample 110 r, then inpainting is deemedcompleted for that test sample area. Otherwise, iterative inpaintingwill continue. It should be noted that different threshold levels may beused in different embodiments.

The comparison between the test sample 110 t (with voids) and thereference sample 110 r (without voids) is made possible by theholographic properties of the K-space data. That is, any given subset ofthe K-space data set 55 will produce the same-image in image space asthe entire K-space data set, just at a reduced resolution level (i.e.,with more distortion). Therefore, by comparing two comparably sizedsamples of the K-space data, one of which has substantially no voids(i.e., the reference sample 110 r) and that other which has a void(s)that is being inpainted (i.e., the reference sample 110 t), it can bedetermined when the accuracy of the inpainted sample area adequatelycompares with that of the reference sample area for stopping purposes.

As discussed further above, the completed reconstructed geospatial modelfrequency domain data set may be transformed into a reconstructedgeospatial model spatial domain data set for display, at Blocks210′-211′. It should also be noted that different approaches forselecting samples may be used instead of the grid method described abovewith reference to FIG. 11. By way of example, a reference sample 110 r′may be selected that is in between spaced apart voids (i.e., an areawithout voids), as seen in FIG. 12. Other suitable approaches forselecting reference samples may also be used, as will be appreciated bythose skilled in the art. It should be noted that the foregoing stoppingtechnique may be used with or without the windowing and waveletdecomposition techniques described above.

Referring now additionally to FIGS. 13 and 20-21, another advantageousaspect for selectively changing inpainting functions used for theinpainting operations is now described. As seen in FIG. 13, one exampleof different inpainting functions that may be used are differentinpainting geometries, such as the illustrated circular and trapezoidalboundary areas 121 and 122 of a K-space geospatial data set 120. Moreparticularly, the inpainting module 40 may perform inpainting withineach of the individual boundary areas 121 and 122 until inpainting iscomplete. However, using different boundary shapes may advantageouslyprovide more accurate inpainting in different embodiments depending uponthe particular shapes and/or sizes of the voids 123 to be inpainted, aswill be appreciated by those skilled in the art. Different inpaintinggeometries may be used at different locations in a same data set, asshown in some embodiments, or the same geometry may be selectively usedthroughout in a given embodiment.

Another inpainting function that can be selectively changed is theinpainting model equation or algorithm being used. As noted above,different modeling equations such as functional PDEs, stochastic models,Navier-Stokes', etc., may be used for different data sets, and/or fordifferent locations within a same data set. The choice of whichgeometry, inpainting equation, etc., to use will generally depend uponfactors such as the smoothness of the data to be inpainted, the size ofthe voids to be inpainted, the desired accuracy level, processingconstraints, etc., as will be appreciated by those skilled in the art.

An exemplary approach for determining which inpainting function(s) touse for inpainting a given set of frequency domain model data 120 beginsat Block 220 with selecting and transforming a reference sample of themodel data into a corresponding reference sample spatial domain dataset, at Block 221. Data is inpainted into one or more voids 123 of thedata set 120 based upon one or more initial selected inpaintingfunctions from among a plurality thereof, as described above, at Blocks222, 222′. More particularly, there may be a plurality of differentinpainting function types (e.g., inpainting boundary geometry,inpainting equation, etc.), and for each type there may be a pluralityof different functions, as noted above. Thus, the processor 32 mayselect not only from among different function types, but for eachfunction type may also advantageously select from a plurality ofdifferent functions within the function type.

A test sample of the inpainted model frequency domain data is selectedand transformed into a corresponding test sample spatial domain dataset, at Block 223. Similar to the above-described stopping approach, thereference sample is then compared with the test sample to determinewhether a new inpainting function (and/or function type) is required,e.g., based upon a threshold difference between the two, as describedabove (Blocks 225, 225′). If the initial function does not provide thedesired accuracy/results, then a new inpainting function is selectedaccordingly, at Block 226′, and the test sample is inpainted once againbased thereon. Once the desired accuracy is obtained, the inpaintedmodel frequency domain data set is transformed into a correspondingspatial domain data set (Block 228′) for display on the display 33, atBlock 229, thus concluding the illustrated method (Block 227, 227′).

Additional features of the invention may be found in copendingapplications entitled GEOSPATIAL MODELING SYSTEM PROVIDING WINDOWEDGEOSPATIAL MODEL DATA INPAINTING AND RELATED METHODS, attorney docketnumber GCSD-1975 (61637); GEOSPATIAL MODELING SYSTEM PROVIDING WAVELETDECOMPOSITION AND INPAINTING FEATURES AND RELATED METHODS, attorneydocket number GCSD-1976 (61638); and GEOSPATIAL MODELING SYSTEMPROVIDING INPAINTING WITH STOPPING METRIC AND RELATED METHODS, attorneydocket number GCSD-1977 (61639), the entire disclosures of which arehereby incorporated herein by reference.

Many modifications and other embodiments of the invention will come tothe mind of one skilled in the art having the benefit of theteachings-presented in the foregoing descriptions and the associateddrawings. Therefore, it is understood that the invention is not to belimited to the specific embodiments disclosed, and that modificationsand embodiments are intended to be included within the scope of theappended claims.

1. A geospatial modeling system comprising: a geospatial model datastorage device; and a processor cooperating with said geospatial modeldata storage device for selecting and transforming a reference sample ofa geospatial model frequency domain data set into a correspondingreference sample geospatial model spatial domain data set, inpaintingdata into at least one void of the geospatial model frequency domaindata set based upon an initial selected inpainting function from among aplurality of different inpainting functions, selecting and transforminga test sample of the inpainted geospatial model frequency domain dataset into a corresponding test sample geospatial model spatial domaindata set, and comparing the reference sample geospatial model spatialdomain data set and the test sample geospatial model spatial domain dataset to determine whether to repeat the inpainting using a differentinpainting function from among the plurality thereof.
 2. The geospatialmodeling system of claim 1 wherein the inpainting functions are basedupon different inpainting boundary geometries.
 3. The geospatialmodeling system of claim wherein the inpainting functions comprisedifferent inpainting models.
 4. The geospatial modeling system of claimwherein the different inpainting models comprise at least one of afunctional partial different equation model and a stochastic model. 5.The geospatial modeling system of claim 1 wherein said processor furthercooperates with said geospatial model storage device for transformingthe inpainted geospatial model frequency domain data set into ageospatial model spatial domain data set.
 6. (canceled)
 7. Thegeospatial modeling system of claim 1 wherein said processor determineswhether to repeat the inpainting using a different inpainting functionbased upon a threshold similarity between the test sample and thereference sample.
 8. The geospatial modeling system of claim 1 whereinthe geospatial model frequency domain data set comprises syntheticaperture radar (SAR) data.
 9. The geospatial modeling system of claim 1wherein the geospatial model frequency domain data set comprises K-spacedata.
 10. The geospatial modeling system of claim 1 wherein saidprocessor inpaints by propagating contour data from outside the at leastone void along a direction of lines of constant contour from outside theat least one void into the at least one void.
 11. (canceled) 12.(canceled)
 13. A geospatial modeling system comprising: a geospatialmodel data storage device; and a processor cooperating with saidgeospatial model data storage device for selecting and transforming areference sample of a geospatial model frequency domain data set into acorresponding reference sample geospatial model spatial domain data set,inpainting data into at least one void of the geospatial model frequencydomain data set based upon an initial selected inpainting function fromamong a plurality of different inpainting functions, selecting andtransforming a test sample of the inpainted geospatial model frequencydomain data set into a corresponding test sample geospatial modelspatial domain data set, comparing the reference sample geospatial modelspatial domain data set and the test sample geospatial model spatialdomain data set to determine whether to repeat the inpainting using adifferent inpainting function from among the plurality thereof basedupon a threshold similarity between the test sample and the referencesample, and transforming the inpainted geospatial model frequency domaindata set into a geospatial model spatial domain data set.
 14. Thegeospatial modeling system of claim 13 wherein the inpainting functionsare based upon at least one of different inpainting boundary geometriesand different inpainting models.
 15. The geospatial modeling system ofclaim 13 wherein the geospatial model frequency domain data setcomprises synthetic aperture radar (SAR) data.
 16. (canceled)
 17. Amodeling system comprising: a model data storage device; and a processorcooperating with said model data storage device for selecting andtransforming a reference sample of a model frequency domain data setinto a corresponding reference sample model spatial domain data set,inpainting data into at least one void of the model frequency domaindata set based upon an initial selected inpainting function from among aplurality of different inpainting functions, selecting and transforminga test sample of the inpainted model frequency domain data set into acorresponding test sample model spatial domain data set, and comparingthe reference sample model spatial domain data set and the test samplemodel spatial domain data set to determine whether to repeat theinpainting using a different inpainting function from among theplurality thereof.
 18. The modeling system of claim 17 wherein theinpainting functions are based upon at least one of different inpaintingboundary geometries and different inpainting models.
 19. The modelingsystem of claim 17 wherein said processor further cooperates with saidmodel storage device for transforming the inpainted model frequencydomain data set into a model spatial domain data set.
 20. The modelingsystem of claim 19 wherein the model frequency domain data set comprisesK-space data.
 21. A geospatial modeling method comprising: selecting andtransforming a reference sample of a geospatial model frequency domaindata set into a corresponding reference sample geospatial model spatialdomain data set; inpainting data into at least one void of thegeospatial model frequency domain data set based upon an initialselected inpainting function from among a plurality of differentinpainting functions; selecting and transforming a test sample of theinpainted geospatial model frequency domain data set into acorresponding test sample geospatial model spatial domain data set; andcomparing the reference sample geospatial model spatial domain data setand the test sample geospatial model spatial domain data set todetermine whether to repeat the inpainting using a different inpaintingfunction from among the plurality thereof.
 22. The method of claim 21wherein the inpainting functions are based upon at least one ofdifferent inpainting boundary geometries and different inpaintingmodels.
 23. The method of claim 21 further comprising transforming theinpainted geospatial model frequency domain data set into a geospatialmodel spatial domain data set.
 24. The method of claim 21 whereincomparing comprises determining whether to repeat the inpainting using adifferent inpainting function based upon a threshold similarity betweenthe test sample and the reference sample.
 25. The method of claim 21wherein the geospatial model frequency domain data set comprisessynthetic aperture radar (SAR) data.
 26. The method of claim 21 whereinthe geospatial model frequency domain data set comprises K-space data.27. A modeling method comprising: selecting and transforming a referencesample of a model frequency domain data set into a correspondingreference sample model spatial domain data set; inpainting data into atleast one void of the model frequency domain data set based upon aninitial selected inpainting function from among a plurality of differentinpainting functions; selecting and transforming a test sample of theinpainted model frequency domain data set into a corresponding testsample model spatial domain data set; and comparing the reference samplemodel spatial domain data set and the test sample model spatial domaindata set to determine whether to repeat the inpainting using a differentinpainting function from among the plurality thereof.
 28. The method ofclaim 21 wherein the inpainting functions are based upon at least one ofdifferent inpainting boundary geometries and different inpaintingmodels.
 29. The method of claim 21 further comprising transforming theinpainted model frequency domain data set into a model spatial domaindata set.
 30. (canceled)